Question

Which of the following describes the roots of the polynomial function fx) = (x+ 2)2(x-4)(x+1)3?

Answer 1

The roots are:

$\bullet \ x=-2 \ with \ multiplicity \ of \ 2 \\ \\ \bullet \ x=4 \\ \\ \bullet \ x=-1 \ with \ multiplicity \ of \ 3$

Explanation:

We have the following polynomial function:

$f(x) = (x+2)^2(x-4)(x+1)^3$

The roots of any polynomial functions are those x-values at which the function equals zero. So, in order to find the roots for this function, we set $f(x)=0$. So:

$(x+2)^2(x-4)(x+1)^3=0 \\ \\ \\ So \ we \ have \ the \ product \ of \ some \ factors \ then: \\ \\ The \ roots \ are: \\ \\ \\ \bullet \ x=-2 \ with \ multiplicity \ of \ 2 \\ \\ \bullet \ x=4 \\ \\ \bullet \ x=-1 \ with \ multiplicity \ of \ 3$

Finally, the graph of this function is shown below and the roots are also indicated.

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Parabola: brainly.com/question/10525169

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